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A001894 Number of permutations of {1,...,n} having n-4 inversions (n>=4).

%I A001894 M3484 N1416 #32 Jun 29 2017 19:23:31
%S A001894 1,4,14,49,174,628,2298,8504,31758,119483,452284,1720774,6574987,
%T A001894 25214332,96997223,374153699,1446677555,5605337934,21758936146,
%U A001894 84604366100,329453055975,1284626463105,5015200610785,19601107218591,76685359017750,300294650988857,1176939165980809
%N A001894 Number of permutations of {1,...,n} having n-4 inversions (n>=4).
%C A001894 Sequence is a diagonal of the triangle A008302 (number of permutations of (1,...,n) with k inversions; see Table 1 of the Margolius reference). - _Emeric Deutsch_, Aug 02 2014
%D A001894 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 241.
%D A001894 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.14., p.356.
%D A001894 R. K. Guy, personal communication.
%D A001894 E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
%D A001894 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001894 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001894 G. C. Greubel, <a href="/A001894/b001894.txt">Table of n, a(n) for n = 4..1000</a>
%H A001894 R. K. Guy, <a href="/A000707/a000707_2.pdf">Letter to N. J. A. Sloane with attachment, Mar 1988</a>
%H A001894 B. H. Margolius, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/MARGOLIUS/inversions.html">Permutations with inversions</a>, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
%H A001894 R. H. Moritz and R. C. Williams, <a href="http://www.jstor.org/stable/2690326">A coin-tossing problem and some related combinatorics</a>, Math. Mag., 61 (1988), 24-29.
%H A001894 E. Netto, <a href="/A000707/a000707_1.pdf">Lehrbuch der Combinatorik</a>, Chapter 4, annotated scanned copy of pages 92-99 only.
%F A001894 a(n) = 2^(2*n-5)/sqrt(Pi*n)*Q*(1+O(n^{-1})), where Q is a digital search tree constant, Q = 0.2887880951... (see A048651). - corrected by _Vaclav Kotesovec_, Mar 16 2014
%e A001894 a(5)=4  because we have 21345, 13245, 12435, and 12354.
%p A001894 f := (x,n)->product((1-x^j)/(1-x),j=1..n); seq(coeff(series(f(x,n),x,n+2),x,n-4), n=4..40); # Barbara Haas Margolius, May 31 2001
%t A001894 Table[SeriesCoefficient[Product[(1-x^j)/(1-x),{j,1,n}],{x,0,n-4}],{n,4,25}] (* _Vaclav Kotesovec_, Mar 16 2014 *)
%Y A001894 Cf. A008302, A048651.
%K A001894 nonn
%O A001894 4,2
%A A001894 _N. J. A. Sloane_
%E A001894 More terms, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001
%E A001894 Definition clarified by _Emeric Deutsch_, Aug 02 2014